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For the case where the disease is a recessive trait (more likely), the probability is 1/2 that they will carry the diseased gene but not show it. If the disease is a dominant trait, the probability is 1/2 that they will get it and show it. Having said that, in the recessive case, if both parents are carriers, then there is a 1/4 case the child will get it from both and then show the disease.

I have answered regarding genetically-transmitted diseases. Mental illness and other forms of "disease" will be different.

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